Target recognition and pattern classification involves the evaluation of new observations on the basis of past observations to distinguish targets or desired patterns from background clutter. This task is complicated by the complex and non-stationary nature of real world environments. Moreover, the computational overhead of many practical classification problems strain serial computer resources.
With respect to the inherent complexity of pattern classification problems, the nonstationary nature of many classification problems makes acquiring a representative data set for training a classifier difficult. The likelihood that the classification scheme would be able to recognize the desired pattern is small without representative training data. This robustness issue is central to pattern recognition solutions in radar identification, speech recognition, and automatic target recognition. In radar identification, parameters describing a radar emitter vary dramatically, as warring parties deliberately change the frequencies and pulse repetition intervals from their peace-time values to disguise the identity of the emitter. In speech recognition, the meanings and sounds of words and phrases change as a function of the culture (or dialect), speaker, or context. In the automatic recognition of targets, targets exist in a vast array of settings, lighting conditions, times of the day and year, orientations, and positions.
With respect to the computational requirements, neural networks provide parallel computational implementations. These networks embody an approach to pattern recognition and classification based on learning. Example patterns are used to train these networks to isolate distinctions between the particular patterns and background clutter for proper classification.
In particular, D. F. Specht in the article "Probalistic Neural Networks and the Polynomial Adaline as Complementary Techniques for Classification," IEEE Transactions on Neural Networks, vol. 1, pp.1 111-120 (1990) discussed the straightforward implementation or mapping of a Parzen estimator the probabilistic neural network into a neural network architecture. His implementation required the network size to be large enough to accommodate all training points such that there is a one-to-one correspondence between the number of nodes in the hidden layer of the network and the number of training points. Specht discusses one approach, the Polynomial Adaline, to reduce the size of the network. In particular, he stated:
The training rule for the polynomial Adaline is derived through a Taylor's series expansion of the PNN decision boundary expressed in terms of sums of exponentials . . . . The result is a general polynomial that describes the decision surface in multidimensional measurement space, and an algorithm for calculating the coefficients of the polynomial based on the training samples . . . . In large, mature applications in which the advantages of economy of hardware and testing speed justify the effort required to select the coefficients which are significant for a particular application, the Padaline is a better choice.
He also noted "the effort required to select the coefficients are significant for a particular application." Moreover, his method does not address the more general problem of mapping any statistical classifier into a parallel architecture.